Stochastic local operations and classical communication equations and classification of even $n$ qubits

TL;DR

This paper develops SLOCC equations and polynomials for classifying entanglement in even $n$ qubits, proposing new genuine entangled states and analyzing their inequivalence to known states.

Contribution

It introduces four SLOCC equations and polynomials for even $n$ qubits, aiding in entanglement classification and state differentiation.

Findings

Four SLOCC equations and polynomials constructed for even $n$ qubits.

New genuine entangled states proposed and distinguished from known states.

Polynomials' absolute values serve as entanglement measures.

Abstract

For any even $n$ qubits we establish four SLOCC equations and construct four SLOCC polynomials (not complete) of degree $2^{n/2}$, which can be exploited for SLOCC classification (not complete) of any even $n$ qubits. In light of the SLOCC equations, we propose several different genuine entangled states of even $n$ qubits and show that they are inequivalent to the $|GHZ>$, $|W>$, or $|l,n>$ (the symmetric Dicke states with $l$ excitations) under SLOCC via the vanishing or not of the polynomials. The absolute values of the polynomials can be considered as entanglement measures.